Question

(2a). According to the Ministry of Health, the height of Guinean travellers who were quarantined in Tamale
for the novel coronavirus were normally distributed about a mean of 160cm and a standard deviation
of 8cm. Find the probability that a traveller selected at random has

i) Height between 148cm and 175cm
ii) Height above 164cm
iii) Height below 179cm

Answer 1

a) Height between 148 cm and 175 cm 

$Z(x =148 ) +Z(x=175)= Z(\frac{148-160}{8})+Z(\frac{175-160}{8}) = Z(-1.5)+Z(1.87)=0.06681+0.96926=1.036$

b) Height above 164 cm  

$=0.5-Z(x =164) = 0.5-Z(\frac{164-160}{8})=0.5-Z(0.5) = 0.5-0.69146= -0.19146$

c) Height below 179 cm

$Z(x = 179) = Z(\frac{179-160}{8})= Z(2.375) =$ 0.99111